Purpose - To investigate the cause of a well-known phenomenon associated with a range of parallel iterative solvers - the variability in the number of iterations required to achieve convergence. Design/methodology/approach - The conclusions are based on extensive experiments undertaken using parallel computers. Recently published works are also used to provide additional examples of variability in iteration count. Findings - The variability of iteration counts experienced by parallelised, element-by-element iterative solvers is caused by numerical precision and roundoff. Research limitations/implications - A theoretical examination of the phenomenon may bring to light a methodology in which the iteration count could be limited to the lower end of the variable range - thus reducing solution times. Practical implications - The authors believe that the variability in iteration count described for element-by-element methods presents no real difficulty to the engineering analyst. Originality/value - The paper gives a detailed account of the phenomenon and is useful both to developers of parallel iterative solvers and to the analysts that use them in practice.
%0 Journal Article
%1 adef1dc9b6434265abe469e992b6468e
%A Smith, Ian M.
%A Margetts, Lee
%D 2006
%I Emerald Group Publishing Ltd.
%J Engineering Computations (Swansea, Wales)
%K myown
%N 2
%P 154--165
%R 10.1108/02644400610644522
%T The convergence variability of parallel iterative solvers
%U https://tinyurl.com/yd42ggj5
%V 23
%X Purpose - To investigate the cause of a well-known phenomenon associated with a range of parallel iterative solvers - the variability in the number of iterations required to achieve convergence. Design/methodology/approach - The conclusions are based on extensive experiments undertaken using parallel computers. Recently published works are also used to provide additional examples of variability in iteration count. Findings - The variability of iteration counts experienced by parallelised, element-by-element iterative solvers is caused by numerical precision and roundoff. Research limitations/implications - A theoretical examination of the phenomenon may bring to light a methodology in which the iteration count could be limited to the lower end of the variable range - thus reducing solution times. Practical implications - The authors believe that the variability in iteration count described for element-by-element methods presents no real difficulty to the engineering analyst. Originality/value - The paper gives a detailed account of the phenomenon and is useful both to developers of parallel iterative solvers and to the analysts that use them in practice.
@article{adef1dc9b6434265abe469e992b6468e,
abstract = {Purpose - To investigate the cause of a well-known phenomenon associated with a range of parallel iterative solvers - the variability in the number of iterations required to achieve convergence. Design/methodology/approach - The conclusions are based on extensive experiments undertaken using parallel computers. Recently published works are also used to provide additional examples of variability in iteration count. Findings - The variability of iteration counts experienced by parallelised, element-by-element iterative solvers is caused by numerical precision and roundoff. Research limitations/implications - A theoretical examination of the phenomenon may bring to light a methodology in which the iteration count could be limited to the lower end of the variable range - thus reducing solution times. Practical implications - The authors believe that the variability in iteration count described for element-by-element methods presents no real difficulty to the engineering analyst. Originality/value - The paper gives a detailed account of the phenomenon and is useful both to developers of parallel iterative solvers and to the analysts that use them in practice.},
added-at = {2018-08-28T15:05:33.000+0200},
author = {Smith, {Ian M.} and Margetts, Lee},
biburl = {https://www.bibsonomy.org/bibtex/2df97d7e8066b0b2da05b7a3bb1aa13d2/leemargetts},
doi = {10.1108/02644400610644522},
interhash = {feb021f14c8ed4b7e82facb7bfcb459a},
intrahash = {df97d7e8066b0b2da05b7a3bb1aa13d2},
issn = {0264-4401},
journal = {Engineering Computations (Swansea, Wales)},
keywords = {myown},
language = {English},
number = 2,
pages = {154--165},
publisher = {Emerald Group Publishing Ltd.},
timestamp = {2020-07-06T23:20:01.000+0200},
title = {The convergence variability of parallel iterative solvers},
url = {https://tinyurl.com/yd42ggj5},
volume = 23,
year = 2006
}